M. M. Grinenko, “Mori Structures on a Fano Threefold of Index 2 and Degree 1”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 116–141; Proc. Steklov Inst. Math., 246 (2004), 103

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 246, Pages 116–141 (Mi tm149)

This article is cited in 19 scientific papers (total in 19 papers)

Mori Structures on a Fano Threefold of Index 2 and Degree 1

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (338 kB) Citations (19)

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Abstract: It is proved that the Mori structures on a nonsingular Fano threefold of index 2 and degree 1 are represented precisely by this Fano variety itself and by fibrations into del Pezzo surfaces of degree 1 that emerge from the blowups of curves of arithmetic genus 1 and degree 1. In particular, such a Fano variety is nonrational and all its birational automorphisms are regular.

Received in February 2004

Bibliographic databases:

Document Type: Article

UDC: 512.763

Language: Russian

Citation: M. M. Grinenko, “Mori Structures on a Fano Threefold of Index 2 and Degree 1”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 116–141; Proc. Steklov Inst. Math., 246 (2004), 103–128

Citation in format AMSBIB

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\by M.~M.~Grinenko

\paper Mori Structures on a~Fano Threefold of Index~2 and Degree~1

\inbook Algebraic geometry: Methods, relations, and applications

\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences

\serial Trudy Mat. Inst. Steklova

\yr 2004

\vol 246

\pages 116--141

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm149}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2101287}

\zmath{https://zbmath.org/?q=an:1120.14031}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2004

\vol 246

\pages 103--128

Linking options:

https://www.mathnet.ru/eng/tm149

https://www.mathnet.ru/eng/tm/v246/p116

This publication is cited in the following 19 articles:

Park J., “G(a)-Actions on the Complements of Hypersurfaces”, Transform. Groups, 27:2 (2022), 651–657
Ciliberto C., Zaidenberg M., “Lines, Conics, and All That”, Pure Appl. Math. Q., 18:1 (2022), 101–176
Cheltsov I. Park J. Prokhorov Yu. Zaidenberg M., “Cylinders in Fano Varieties”, EMS Surv. Math. Sci., 8:1-2 (2021), 39–105
Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
Cheltsov I., Dubouloz A., Park J., “Super-Rigid Affine Fano Varieties”, Compos. Math., 154:11 (2018), 2462–2484
Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1-2 (2016), 721–782
Beauville A., “The Luroth Problem”, Rationality Problems in Algebraic Geometry, Lect. Notes Math., Lecture Notes in Mathematics, 2172, eds. Pardini R., Pirola G., Springer International Publishing Ag, 2016, 1–27
A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
Kishimoto T., Prokhorov Yu., Zaidenberg M., “Affine Cones Over Fano Threefolds and Additive Group Actions”, Osaka J. Math., 51:4 (2014), 1093–1112
Debarre O., Iliev A., Manivel L., “On the Period Map for Prime Fano Threefolds of Degree 10”, J Algebraic Geom, 21:1 (2012), 21–59
Hausen J., Herppich E., Suess H., “Multigraded Factorial Rings and Fano Varieties with Torus Action”, Doc Math, 16 (2011)
A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171
I. A. Cheltsov, K. A. Shramov, “Extremal Metrics on del Pezzo Threefolds”, Proc. Steklov Inst. Math., 264 (2009), 30–44
M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300
V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421
I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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